Introduction to NODAL Analysis (1)

7/29/2019 Introduction to NODAL Analysis (1)

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Introduction to NODALanalysis


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Learning Objectives

Inflow Performance Relationship (IPR) Single phase

Two phase

Vertical Lift Performance Single phase

Two phase

Flow Through Chokes

Matching Inflow and Tubing Performances


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Introduction

Production by natural flow Need for better understanding of various concepts

which define well performance. Pressure loss occurs in:

the reservoir the bottom hole completion the tubing or casing the wellhead the flowline the flowline choke pressure losses in the separator and export pipeline to

storage


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Introduction Production is generally limited by the pressure in the reservoir

and difficult to do something about it. A major task is to optimise the design to maximise oil and gas

recovery.


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Production Performance

Production performance involves matchingup the following three aspects: Inflow performance of formation fluid flow from

formation to the wellbore.

Vertical lift performance as the fluids flow up thetubing to surface.

Choke or bean performance as the fluids flowthrough the restriction at surface.


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Fluid Flow Through Porous Media

The ability to determine the productivity of a reservoirand the optimum strategy to maximise the recoveryrelies on an understanding of the flow characteristicsof the reservoir and the fluid it contains.

The interaction between the fluid (and its properties)

and the rock (and its properties) Comparison with flow through pipes.

Multiple fluids Surface tension

Capillary forces


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Fluid Flow Through Porous Media

The nature of the fluid flow Time taken for the pressure change in the reservoir Fluid to migrate from one location to another For any pressure changes in the reservoir, it might

take days, even years to manifest themselves inother parts of the reservoir.

Therefore flow regime would not be steady state Darcys law could not be applied Time dependent variables should be examined


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Two Phase Flow, Vogels Equation

2

r

wf

r

wf

maxo

o )P

P(8.0)

P

P(2.01

q

q=

A simplified solution was offered by Vogel. He simulated the PVT

properties and cumulative production from different wells on computer to

produce many IPR curves. These were then normalised for pressure and

producing rate. The curves produced represent many different depletion

drive reservoir. A single curve can be fitted to the data with the following

equation.

This equation has been found to be a good representation of many

reservoirs and is widely used in the prediction of IPR curves for 2-phaseflow. Also, it appears to work for water cuts of up to 50%.


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Vogels Equation, Example-1

b/d211)2400800(8.0)

2400800(2.01250)

PP(8.0)

PP(2.01qq

psi800PFor

b/d250

)2400

1800(8.0)

2400

1800(2.01

100

)P

P(8.0)

P

P(2.01

qq

psi1800P

b/d100q

psi2400P

:datafollwoingthegivenpsi,800PforqandqFind

22

r

wf

r

wfmaxoo

22

r

wf

r

wf

omaxo

wf

o

r

wfoomax

= = =

=

=

=

=

=

=

=

=


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Vogels Equation, Example, Cont.

If other values of Pwf

are chosen, sufficient

qos can be generated

to plot the curve, e.g.:

Pwf qo800 211

1200 175

1600 128

2000 69

IPR

0

500

1000

1500

2000

2500

3000

0 100 200 300qo

Pwf


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Vogels Equation, Combined Single Phase Liquid

and 2-Phase

In this case there is a single

phase liquid which exists

above the bubble point. Below

the bubble point the system

becomes 2-phase.

The figure opposite shows the

IPR, which is a combined

linear-Vogel plot (i.e., straight

line above Pb and Vogel

below Pb with Pb substitutedfor Pr).

Pb

Pr

qb qmaxq

Pwf

Straight line above Pb

Vogel below Pb


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Vogels Equation, Example-2

psia1000b.psia2500a.:ofPforqiii)

PbelowIPRVogelassuming,q)qi)

:Find

)4

3(ln

)(1008.7

cp0.682.1B0S

ft0.4rft2000rft60h

md30kpsia2000Ppsia3000P

:datafollwoingGiven the

wfo

bmax

b

3

o

we

b

ii

r

rB

PPhkq

w

eoo

wfsro

o

o

r

=

===

======


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Example-2, Solution

=

=+

=

=

2

max

b

3

3

)(8.0)(2.01

PbeyondVogelusingii)

b/d2010

)04

3

4.0

2000(ln2.168.0

)20003000(60301008.7

)

4

3(ln

)(1008.7

:usedisequationinflowradialforethere

point,bubbletheabovePIgivennoisTherei)

r

wf

r

wf

oo

w

eoo

wfsro

o

P

P

P

Pqq

r

rB

PPhkq


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Example-2, Solution

b/d/psi01.220003000

2010PatPItherefore

8.1

PPI)Vogel(q

P

8.1q

P

P6.1

P

2.0q

dP

qd-PIPPatand

P

P6.1

P

2.0q

dP

qd-

P

P6.1

P

2.0q

dP

qd

PI.thegivesitateddifferentiisequationsVogel'ifIPR,theofslopetheisPIthethatmemberingRe

b

bmaxo

b

maxo2b

b

b

maxo

wf

obwf

2

r

wf

rmaxo

wf

o2

r

wf

rmaxo

wf

o

=

=

=

=

+===

+=

=


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Example-2, Solution

b/d357315632010qqq

b/d1563)200010000.8()

20001000(2.01qq

Pi.e.psi,1000Pb.

b/d1005)25003000(01.2)PPPI(q

,Pi.e.psi,2500Pa.iii)

b/d424322332010qqq

b/d22338.1

200001.28.1

PPIq

o(Vogel)bo(total)

2)Vogelmax(o(Vogel)

bwf

wfr

bwf

)vogelmax(b)totalmax(

b)vogelmax(o

=+=+=

= =

=

=+=+=

===


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Vogels Equation, Problems-1&2

IPRthePlot

b/d/psi2PIpsi3000P

psi4200P

psi.2500Pforqand,q,qfinddata,followingtheUsing

2-Problem

_______________________________________

psig1000Pb/d150q

psig1600Ppsig1600P

:datafollowingtheforIPRplotandqFind

1-Problem

b

r

wfmax(total)b

wfo

br

omax

==

=

=

==

==


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Two Phase Flow: Effect of GOR


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Non Darcy Flow

Darcys law only applies to laminar flow situations, a valid

assumption for the majority of oil wells. For gas wells and some very high flowrate (light crude) oil

wells, the volumetric expansion as fluid approaches the

wellbore is very high and this can result in turbulent flow.

In such cases, a modified form of the Darcy equation,

known as the Forchheimer equation, is used:

2U

K

U

dr

dP+

=

The non-Darcy component due to turbulent flow is

normally handled as an additional pressure loss PND


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Productivity Index (PI)

Productivity index is a measure of the capability of a

reservoir to deliver fluids to the bottom of a wellbore.

It relates the surface production rate and the pressure drop

across the reservoir, known as the drawdown.

To take into account the effect of the thickness of producing

interval and comparison of various wells, the Specific

Productivity Index is defined as:


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PI For SS Incompressible Flow

PI is constant if, B and K remain constant. Plot of Pwversus qs should be a straight line of slope 1/J, with

an intercept on the ordinate axis of Pe.

PI for Semi-Steady State Incompressible Flow

)rrln(B

Kh10082.7

PP

q

J)PI(

w

e

3

we

s

SSSS

===


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Oil Wells Productivity Index

The Productivity Index (PI)is the ratio ofproduction to the pressure draw down at the mid-point of the production interval

rateflowoilQpresureflowingP

presurestaticPPP

QPI

owf

wiwfwi

o

==

=

=

The productivity index is a measure of the oil well potential or ability

to produce and is a commonly measured well property.

PI is expressed either in stock tank barrel per day per psi or in

stock tank cubic metres per day per kPa.


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Practical determination of PI

The static pressure (Pwi

) is measured by:

prior to open a new well (after clean up)

after sufficient shut in period (existing wells)

In both cases a subsurface pressure gauge is run into

the well

The flowing bottom hole pressure (Pwf) is recorded

after the well has flowed at a stabilised rate for a

sufficient period (new wells)

prior to shut in for the existing wells


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Decline of PI at High Flow Rates

In most wells the productivity index remains

constant over a wide range of variation inflow rate. Therefore, the oil flow rate isdirectly proportional to bottom hole

pressure draw down.

However, at high flow rate the linearity failsand the productivity index declines, whichcould be due to:

1- turbulence at high volumetric flow rates

2- decrease in relative permeability due tothe presence of free gas caused by the dropin pressure at the well bore

3- the increased in oil viscosity withpressure drop below bubble point

Flow rate

PI

Drawdown

Qo PI


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Example 1

A well has a shut in bottom hole pressure of 2300 psia and

produces oil at 215 barrels/day under a draw down of 500 psi.

The well produces from a formation of 36 feet net productive

thickness. What is productivity index, and specific productivity

index?

Specific productivity index

Productivity Index is a function of productive thickness (in fact,the length of perforation interval). In order to compare thewells with each other, the specific productivity index (PI)s isdefined as:

ions)(performatzonepaytheoflengthh

)PP(h

QhPI)PI(

wfwi

os

=

==


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Tubing Performance

The pressure loss in the tubing can be a significant

proportion of the total pressure loss. However its

calculation is complicated by the number of

phases which may exist in the tubing.

It is possible to derive a mathematical expressionwhich describes fluid flow in a pipe by applying

the principle of conservation of energy.

The principle of the conservation of energyequates the energy of fluid entering in and exiting

from a control volume.


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Fundamental Derivation of Pipe Flow Equation

The principle of the conservation of energy equates

the energy of fluid entering and exiting from a controlvolume.


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Flow Regimes in Vertical 2-Phase Flow

As the pressure on a crude oil containing gas in solution is

steadily reduced, free gas is evolved and as a consequence, the

liquid volume decreases.

This phenomenon affects the relative volumes of free gas andoil present at each point in the tubing of a flowing well.

If the bottom hole pressure in a well is above the bubble point

of the crude oil, single phase liquid is present in the lower part

of the tubing.


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Flow Regimes in Vertical 2-Phase Flow, Cont.

As the liquid moves up the tubing, thepressure drops and gas bubbles begin toform. This flow regime where gas bubblesare dispersed in a continuous liquidmedium is known as bubble flow.

As the fluid moves further up the tubing,

the gas bubbles grow and become morenumerous. The larger bubbles slip upwardat a higher velocity than the smaller ones,because of the buoyancy effect.

Single Phase

Liquid Flow

Bubble

Flow

Slug or Plug

Flow

Annular

Flow

Mist

Flow


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A stage is reached where these large bubbles extendacross almost the entire diameter of the tubing. As aresult, slugs of oil containing small bubbles areseparated from each other by gas pockets that occupythe entire tubing cross section except for a film of oilmoving relatively slowly along the tubing wall. This isSlug or Plug Flow.

Still higher in the tubing, the gas pockets may havegrown and expanded to such as extent that they areable to break through the more viscous oil slug. Gasforms a continuous phase near the centre of the tubing

carrying droplets of the oil up with it. Along the walls ofthe tubing there is an upward moving oil film. This isAnnular Flow.

Single Phase

Liquid Flow

Bubble

Flow

Slug or Plug

Flow

Annular

Flow

Mist

Flow


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Continued decrease in pressure with resultantincrease in gas volume results in a thinner and thinneroil film, until finally the film disappears and the flowregime becomes a continuous gas phase in which oildroplets are carried along with the gas, i.e., Mist Flow.

Not all these flow regimes will occur simultaneously ina single tubing string, but frequently 2 or possibly 3may be present.

In addition to flow regimes, the viscosity of oil and gasand their variation with pressure and temperature,

PVT characteristics, flowing bottom hole pressure(BHP), and tubing head pressure (THP) affect thepressure gradient. Single Phase

Liquid Flow

Slug or Plug

FlowBubble

Flow

Annular

Flow

Mist

Flow


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These flow patterns have been observed by a number ofinvestigators who have conducted experiments with air-water

mixtures in visual flow columns.

The conventional manner of depicting the experimental data

from these observations is to correlate the liquid and gas

velocity parameters against the physical description of theflow pattern observed.

Such presentations of data are referred to as flow pattern

maps. The map is a log-log plot of the superficial velocities

of the gas and liquid phases.


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Practical Application of Multiphase Flow

Multiphase flow correlations could be used for: Predict tubing head pressure (THP) at various rates

Predict flowing bottom hole pressure (BHP) at various rates

Determine the PI of wells

Select correct tubing sizes Predict maximum flow rates

Predict when a well will die and hence time for artificial lift

Design artificial lift applications

The important variables are: tubing diameter, flowrate, gas liquid

ratio (GLR), viscosity, etc.


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Liquid-Liquid Flow

The case of liquid-liquid flow in production wells may

occur in low GOR wells which produce water.

Since both phases are only slightly compressible or

incompressible, it would be expected that the physical

nature of the flow of an oil-water mixture to surface

would not be as dramatically different from single phaseliquid flow as the oil-gas system.

If oil and water enter the wellbore from the reservoir and

flow up the tubing to surface, the physical distribution of

the phases will depend upon their relative volumetricproperties, ie, one phase will be continuous and the other

dispersed.


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Liquid-Liquid Flow

Unlike the gas therewill be little relativevolumetric expansion

between the twophases.

Thus, the physicaldistribution will bemore dependent onthe WOR and the

flow velocity.


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Pressure Transverse or Gradient Curves

A, B, C=DifferentTubing HeadPressures


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Pressure Transverse or Gradient Curves

By shifting the curves

downwards, he found that, fora constant GLR, flowrate andtubing size, the curvesoverlapped

Then, a single curve could beutilised to represent flow in thetubing under assumedconditions.

The impact was in effect toextend the depth of the well bya length which, would

dissipate the tubing headpressure. A, B, C=Different

Tubing HeadPressures


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Gradient Curves

Gilbert was then able to

collect all the curves for aconstant tubing size and

flowrate on one graph,

resulting in a series of

gradient curves whichwould accommodate a

variety of GLRs.

He then prepared a series

of gradient curves atconstant liquid production

rate and tubing size.


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Gradient Curves


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Positive or Fixed Choke This normally consists of two

parts: A choke which consists of

a machined housing into

which the orifice capability

or "bean" is installed.

A "bean" which consists of

a short length 1-6", of thick

walled tube with a smooth,

machined bore of specified

size.


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Valve Seat with Adjustable Valve Stem

In this design, the orifice

consists of a valve seatinto which a valve stemcan be inserted andretracted, thus adjusting

the orifice size. The movement of the valve

stem can either be manualor automatic using anhydraulic orelectrohydraulic controller.


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Choke Flow Characteristics

Chokes normally operate in multiphase

systems. Single phase can occur in dry gaswells.


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Critical Flow through Chokes

R=P2/P1The value of R at the

point where the

plateau production

rate is achieved istermed the

critical pressure ratio

Rc.


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Critical Flow through Chokes

Critical flow behaviour is only exhibited by highly

compressible fluid such as gases and gas/liquid mixtures. For gas, which is a highly compressible fluid, the critical

downstream pressure Pc is achieved when velocity

through the vena contracta equals the sonic velocity this means that a disturbance in pressure or flow

downstream of the choke must travel at greater than thespeed of sound to influence upstream flow conditions.

In general, critical flow conditions will exist whenRc=


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Multiphase Flow through a Choke A number of researchers have published studies on

multiphase flow through chokes. Some of the studies relate to correlation of field

measurements.

PTH = tubing head flowing pressure in psia

Cd = constant

R =gas liquid ratio (MSCF/bbl)Q =oil flowrate (STB/d)

S =bean size in 1/64"

Gilbert (435 is correct)

Achong (R in SCF/bbl)


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Matching the Inflow and Tubing Performance

Method 1 - Reservoirand tubing pressure loss

convergence in

predicting bottomhole

flowing pressure


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Matching the Inflow and Tubing Performance


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Introduction to NODAL Analysis (1)

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